Were there any that were not from you? — Banno
I mostly ignore users who run into a thread shitting on everyone in sight who is not a mod, and that's what I largely did when Tones entered. — Leontiskos
I mostly ignore users who run into a thread shitting on everyone in sight who is not a mod, and that's what I largely did when Tones entered. — Leontiskos
You ignored him for twenty-odd pages? — Banno
There may be something in what you are attempting to articulate. Perhaps a difference between Aristotelian logic and prop calculus could be shown in some interesting way. But quite a few of your comments were simply demonstrably incorrect. This thread was a lsot opportunity for you. — Banno
MP and MT are commensurable with ancient (and colloquial) logic in a way that RAA is not. — Leontiskos
Can you show this using Prop logic? If not, then why can't it be dismissed as an artefact of the limitations of Aristotelian logic?RAA directly leverages the LEM in an entirely unique way. — Leontiskos
RAA directly leverages the LEM in an entirely unique way. — Leontiskos
Suppose (1) p ⊢ ~p
(2) ⊢p → ~p from (1)
(3) ⊢p → (p & ~p) from (2) since p →p
(4) ⊢ ~(p & ~p) → ~p from (3) by contraposition
(5) ⊢ ~(p & ~p) by the Law of Contradiction
(6) ⊢ ~p from (4), (5) by modus ponens
Deriving RAA from MT, and MT from RAA are common introductory exercises. — Banno
Can you show this using Prop logic? If not, then why can't it be dismissed as an artefact of the limitations of Aristotelian logic? — Banno
IEP gives this as the form of the reductio:
If p ⊢ ~p, then ⊢ ~p — Banno
I'll invite you to set out an example. It might be helpful....in a dialogical context (which is my primary context) a MP cannot be rebuffed, but a reductio can. — Leontiskos
Deriving RAA from MT [...] are common introductory exercises. — Banno
ρ→(φ^~φ) (premise)
~(φ^~φ) (law of non contradiction)
:. ~ρ (modus tollens) — flannel jesus
and part of the difficulty here is that an absurdity and a contradiction are not synonyms in the historical senses of reductio ad absurdum. Metaphysical and logical absurdities are both utilized historically under that name.) — Leontiskos
whether RAA can be derived from MT, and this is not at all apparent. — Leontiskos
It would be hard to dispatch Tones' army of strawmen. — Leontiskos
I almost guarantee that Aristotle will see a reductio as a metabasis eis allo genos — Leontiskos
creative attempts to justify reductio in classical propositional logic. — Leontiskos
Laymen and logicians alike are on occasion apt to say, "An absurdity? A contradiction? So what? 'I contain multitudes'." — Leontiskos
I'll invite you to derive RAA from MT as a way to engage with what I've already written. — Leontiskos
It becomes primarily a way to elaborate and extend a system. — Leontiskos
Laws of deduction are not usually derived from one another. — Banno
Actually, there've been other first insulters in this thread. — TonesInDeepFreeze
That last clause is wrong, obviously. (Maybe you corrected it subsequently.) — TonesInDeepFreeze
Now, the conclusion that I arrived at is that "A does not imply a contradiction" is not an accurate statement about ¬(A→(B and ¬B)), it would be a true statement about (A→¬(B and ¬B)) instead. — Lionino
All you [another poster] need to do is provide such a derivation. — Leontiskos
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